{"paper":{"title":"Multivariate Normality of a class of statistics based on extreme observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gane Samb Lo","submitted_at":"2012-02-12T17:47:25Z","abstract_excerpt":"Let $X_{1},X_{2},...$ be a sequence of independent random variables ($rv$)with common distribution function ($df$) $F$ such that $F(1)=0$ and for each $n\\geq 1,$ let $X_{1,n}\\leq X_{2,n}\\leq ...\\leq X_{n,n}$ denote the order statistics based on the n first of these random variables. L\\^{o} (\\cite{gslod}) introduced a class of statistics aimed at characterizing the asymptotic behavior of the univatiate extremes. This class this estimator of the square of the extremal index of a $df$ lying in the extremal domain of attraction :\n  $$ k^{-1}\\sum_{j=\\ell +1}^{j=k}\\ \\sum_{i=j}^{i=k}i(1-\\delta_{ij}/2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2550","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}